Multiply 8674 x 678 is what

Kiersten runs a website that helps people learn programming. Every month, Kiersten receives a subscription fee of \$10$10dollar

bogdanovich [222]

Answer:

sorry but it is wrong the answer is 1,200

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Mrs.Steﬀen’s third grade class has 30 students in it. The students are divided into three groups(numbered 1, 2,and 3),each havin

qaws [65]

Answer:

a. $\\ 10! = 3628800$ ;

b. $\\ 10!*10!*10! = 47784725839872000000 = 4.7784725839872*10^{19}$

Step-by-step explanation:

We need here to apply the Multiplication Principle or the Fundamental Principle of Counting for each answer. Answer b needs an extra reasoning for being completed.

The Multiplication Principle states that if there are n ways of doing something and m ways of doing another thing, then there are n x m ways of doing both (Rule of product (2020), in Wikipedia).

<h3>In how many ways can ten students line up? </h3>

There are ten students. When one is selected, there is no other way to select it again. So, no repetition is allowed.

Then, in the beginning, there are 10 possibilities for 10 students; when one is selected, there are nine possibilities left. When another is selected, eight possibilities are left to form the file, and so on.

Thus, we need to multiply the possibilities after each selection: that is why the Multiplication Principle is important here.

This could be expressed mathematically using n!:

$\\ n! = n * (n-1)! * (n-2)! *...* 2*1.$

For instance, $\\ 5! = 5 * (5-1)! * (5-2)! *...*2*1 = 5 * 4 * 3 * 2 * 1 = 120.$

So, for the case in question, the ten students can line up in:

$\\ 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800$ ways to line up in a single file.

<h3>Second Question</h3>

For this question, we need to consider the former reasoning with extra consideration in mind.

The members of Group 1 can occupy only the following places in forming the file:

$\\ G1 = \{ 1, 4, 7, 10, 13, 16, 19, 22, 25, 28\}^{th}$ places.

The members of Group 2 only:

$\\ G2 = \{ 2, 5, 8, 11, 14, 17, 20, 23, 26, 29\}^{th}$ places.

And the members of Group 3, the following only ones:

$\\ G3 = \{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30\}^{th}$ places.

Well, having into account these possible places for each member of G1, G2 and G3, there are: 10! ways for lining up members of G1; 10! ways for lining up members of G2 and, also, 10! ways for lining up members of G3.

After using the Multiplication Principle, we have, thus:

$\\ 10! * 10! * 10! = 47784725839872000000 = 4.7784725839872 *10^{19}$ ways the students can line up to come in from recess.

3 0

2 years ago

A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlar

OverLord2011 [107]

Answer:

The area of the enlarged triangle is $4$ times the original area

Step-by-step explanation:

we know that

The scale factor is equal to divide the measurement of the length side of the enlarged triangle by the the measurement of the length of the corresponding side of the original triangle

In his problem

Let

x------> the length side of the original triangle

so

2x-----> is the length of the corresponding side of the enlarged triangle

$scale\ factor=\frac{2x}{x}=2$

$scale\ factor> 1$ -------> that means is increasing

The scale factor squared is equal to the ratio of the area of the enlarged triangle divided by the area of the original triangle

so

Let

m-------> the area of the enlarged triangle

n------> the area of the original triangle

r-------> scale factor

$r^{2} =\frac{m}{n}$

we have

$r=2$

substitute

$2^{2} =\frac{m}{n}$

$m=4n$

therefore

The area of the enlarged triangle is $4$ times the original area

8 0

2 years ago

Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest

lakkis [162]

Answer:

Option B ,$133.92 is correct

Step-by-step explanation:

By consolidating both balances in Card B,APR of 12% would apply to funds in card A as well

Let us approach the question by solving for monthly payment of Card A using 12% APR as follows while making use of excel pmt formula:

=pmt(rate,nper,-pv,fv)

rate is the monthly rate on the card which is 12%/12=1%

nper is the number of months of payment which is 12 months * 4 years=48

pv is the current balance in the card which is $1,389.47

fv is the total amount of monthly repayment which is taken as zero

=pmt(1%,48,-1389.47,0)=$ 36.59

Using 16% monthly payment is $39.38 which is given already

Total monthly payments for 16%=$39.38*48=$1890.24

Total monthly payments for 12% APR=$36.59*48=$1756.32

savings in total repayments=savings in interest=$1890.24 -$1756.32 =$133.92

4 0

1 year ago

Jamie and Owen joined a monthly walking challenge at their youth center. Jamie has already walked 120 minutes and plans to walk

Soloha48 [4]

I think the best answer would be letter B. Y= 20x and Y= 30x+120. So by calculating it through substitution you will come up to 20x = 30x+120. By simplifying the equation it will give you an answer of 12 days.

7 0

2 years ago